Various apparatus and methods had been proposed in the past for increasing the effective recorded data density on various record media, such as magnetic disks, tapes and optical record media. One accepted approach is known as run-length-limited encoding (RLL) which requires that each binary one (which represents a first signal or record state) in a coded bit sequence be separated from the next occurring binary one by a bounded number of intervening zeros. The number of intervening zeros is equal to a minimum quantity called d and cannot exceed a maximum number of zeros k. Quantity d is to limit inter-symbol interference while the quantity k enables a readback clock to be derived from recorded or transmitted signals. Codes for recording media and communications using this general arrangement are referred to as (d,k) run-length-limited codes. Such codes convert unconstrained data into a (d,k) constrained channel set of signals. Generally, such codes are encoded from m unconstrained bits which are mapped into n constrained bits, where m is less than n. The ratio m/n is referred to as the coding rate. It is obviously desirable to maximize this rate. Information density is defined as (m/n)(d+1).
Increasing the coding rate occurs at the expense of look ahead resulting in increasing error propagation within the channel encoded bits or groups. For example, a single-bit error introduced into the encoded channel code stream can result in a predetermined number of subsequent bits (unconstrained bits) being also erroneous before the encoding algorithm enables the channel code bits to be self-correcting.
The Franaszek, U.S. Pat. No. 3,689,899, discloses two d,k codes which are 1,8 and 2,7. These codes are variable-length fixed-rate state-independent block codes. The coding rate of the 1,8 code was set to be 2/3 with a code dictionary of sixteen code words having lengths varying from three to nine channel bits, all in multiples of three channel bits. The Franaszek 2,7 code has a coding rate of 1/2 with a dictionary of seven channel words varying in length from two channel bits to eight channel bits in multiples of two channel bits. Another reference showing a 1,7 code is "Efficient Code for Digital Magnetic Recording", by Franaszek in the IBM Technical Disclosure Bulletin, Vol. 23, No. 9, Feb. 1981 on page 4375. This reference teaches a bounded delay code. The article "An Optimization of Modulation Codes in Digital Recording", by Horiguchi et al., IEEE Transactions on Magnetics, Vol. MEG-12, No. 6, Nov. 1976, page 740, discloses another d,k code.
The Eggenberger et al., U.S. Pat. No. 4,115,768, avoids the grouping requirement of the Franaszek codes. This patent shows a 2,7 d,k code which avoids the framing requirements. The information density of the 1,7 and 2,7 d,k codes are respectively 1.3 and 1.5. If a 3,7 code is employed, then an information density of 1.6 is found while a 4,20 code results in an information density value of 2.0.